Model checking ω-regular properties for quantum Markov chains

© Yuan Feng, Ernst Moritz Hahn, Andrea Turrini, and Shenggang Ying. Quantum Markov chains are an extension of classical Markov chains which are labelled with super-operators rather than probabilities. They allow to faithfully represent quantum programs and quantum protocols. In this paper, we investigate model checking !-regular properties, a very general class of properties (including, e.g., LTL properties) of interest, against this model. For classical Markov chains, such properties are usually checked by building the product of the model with a language automaton. Subsequent analysis is then performed on this product. When doing so, one takes into account its graph structure, and for instance performs different analyses per bottom strongly connected component (BSCC). Unfortunately, for quantum Markov chains such an approach does not work directly, because super-operators behave differently from probabilities. To overcome this problem, we transform the product quantum Markov chain into a single super-operator, which induces a decomposition of the state space (the tensor product of classical state space and the quantum one) into a family of BSCC subspaces. Interestingly, we show that this BSCC decomposition provides a solution to the issue of model checking ω-regular properties for quantum Markov chains

Formal Verification of Probabilistic SystemC Models with Statistical Model Checking

Transaction-level modeling with SystemC has been very successful in describing the behavior of embedded systems by providing high-level executable models, in which many of them have inherent probabilistic behaviors, e.g., random data and unreliable components. It thus is crucial to have both quantitative and qualitative analysis of the probabilities of system properties. Such analysis can be conducted by constructing a formal model of the system under verification and using Probabilistic Model Checking (PMC). However, this method is infeasible for large systems, due to the state space explosion. In this article, we demonstrate the successful use of Statistical Model Checking (SMC) to carry out such analysis directly from large SystemC models and allow designers to express a wide range of useful properties. The first contribution of this work is a framework to verify properties expressed in Bounded Linear Temporal Logic (BLTL) for SystemC models with both timed and probabilistic characteristics. Second, the framework allows users to expose a rich set of user-code primitives as atomic propositions in BLTL. Moreover, users can define their own fine-grained time resolution rather than the boundary of clock cycles in the SystemC simulation. The third contribution is an implementation of a statistical model checker. It contains an automatic monitor generation for producing execution traces of the model-under-verification (MUV), the mechanism for automatically instrumenting the MUV, and the interaction with statistical model checking algorithms.Comment: Journal of Software: Evolution and Process. Wiley, 2017. arXiv admin note: substantial text overlap with arXiv:1507.0818

Comparing Labelled Markov Decision Processes

A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of equivalence checking for the verification of anonymity, we study the algorithmic comparison of two labelled MDPs, in particular, whether there exist strategies such that the MDPs become equivalent/inequivalent, both in terms of trace equivalence and in terms of probabilistic bisimilarity. We provide the first polynomial-time algorithms for computing memoryless strategies to make the two labelled MDPs inequivalent if such strategies exist. We also study the computational complexity of qualitative problems about making the total variation distance and the probabilistic bisimilarity distance less than one or equal to one

On Correctness, Precision, and Performance in Quantitative Verification: QComp 2020 Competition Report

Quantitative verification tools compute probabilities, expected rewards, or steady-state values for formal models of stochastic and timed systems. Exact results often cannot be obtained efficiently, so most tools use floating-point arithmetic in iterative algorithms that approximate the quantity of interest. Correctness is thus defined by the desired precision and determines performance. In this paper, we report on the experimental evaluation of these trade-offs performed in QComp 2020: the second friendly competition of tools for the analysis of quantitative formal models. We survey the precision guarantees - ranging from exact rational results to statistical confidence statements - offered by the nine participating tools. They gave rise to a performance evaluation using five tracks with varying correctness criteria, of which we present the results

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

Dynamic Verification of SystemC with Statistical Model Checking

Many embedded and real-time systems have a inherent probabilistic behaviour (sensors data, unreliable hardware,...). In that context, it is crucial to evaluate system properties such as "the probability that a particular hardware fails". Such properties can be evaluated by using probabilistic model checking. However, this technique fails on models representing realistic embedded and real-time systems because of the state space explosion. To overcome this problem, we propose a verification framework based on Statistical Model Checking. Our framework is able to evaluate probabilistic and temporal properties on large systems modelled in SystemC, a standard system-level modelling language. It is fully implemented as an extension of the Plasma-lab statistical model checker. We illustrate our approach on a multi-lift system case study